A comparative study of integration algorithms for finite single crystal (visco-)plasticity

Prüger, Stefan; Kiefer, Björn

doi:10.1016/j.ijmecsci.2020.105740

Cited by 14 publications

(12 citation statements)

References 72 publications

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“…The mean-field homogenization scheme is applied to study the effect of martensite inclusions embedded in single-crystalline austensite. To this end, a recently investigated single-crystal plasticity model [6] is adopted in the constitutive description of the individual phases. In particular, in the face-centered cubic austenite the plastic slip is considered on the primary octahedral {111} 110 slip systems, whereas in the body-centered cubic martensite the {110} 111 and the {112} 111 families of slip systems are included.…”

Section: Resultsmentioning

confidence: 99%

Mean‐field homogenization based constitutive modeling of austenitic TRIP‐steels at the single crystal scale

Prüger

Kiefer

2021

Proc Appl Math and Mech

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In order to accurately describe the effective mechanical behavior of single-crystalline, austenitic TRIP-steels, a two-phase mean-field homogenization scheme is presented in a finite deformation framework, which also includes transformationinduced eigendeformations. The constitutive behavior of the two phases, namely austenite and martensite, is described by a rate-independent single-crystal plasticity model that captures elastic anisotropy as well as anisotropic slip and hardening behavior. The response of the two-phase model under homogeneous deformation states is investigated and a particle strengthening effect is predicted in the absence of transformation-induced eigendeformations and a suitable choice of material constants, while upon the inclusion of eigendeformations a gradual stress softening is observed.

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Section: Resultsmentioning

confidence: 99%

Mean‐field homogenization based constitutive modeling of austenitic TRIP‐steels at the single crystal scale

Prüger

Kiefer

2021

Proc Appl Math and Mech

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“…$$ The reader is referred to Reference 7 for more details regarding the augmented Lagrangian approach to the crystal plasticity problem analogous to the present one. The augmented Lagrangian approach also proved useful in other algorithms for crystal plasticity, compare Reference 35.…”

Section: The Algorithmmentioning

confidence: 99%

“…In such cases, the pseudo‐inverse or generalized inverse methods can be used 27,28,30 . Subsequently, other algorithms have been developed, compare References 31‐37 and the references therein. The closest to the present article are the works based on the incremental energy minimization, 6,7,21,38‐47 but they require existence of an incremental potential, which is a separate assumption in the general case.…”

Section: Introductionmentioning

confidence: 99%

Crystal plasticity algorithm based on the quasi‐extremal energy principle

Petryk

Kursa

2022

Numerical Meth Engineering

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The direct incremental energy minimization in rate‐independent plasticity does not account for the skew‐symmetric part of the tangent stiffness matrix. In crystal plasticity, this corresponds to neglecting the asymmetry of the matrix of interaction moduli for active slip‐systems. This limitation has been overcome in the recently proposed quasi‐extremal energy principle (QEP) applicable to nonpotential problems. In the present article it is shown how to extend QEP to finite increments in the backward‐Euler computational scheme. A related constitutive algorithm is proposed which enables automatic selection of active slip systems using an energetic criterion, along any path of large deformation of a rate‐independent single crystal with a nonsymmetric slip‐system interaction matrix. Numerical examples have been calculated for a fcc single crystal subjected to simple shear or uniaxial tension. The slip system activity predicted by using the QEP algorithm has been found to be more reliable in describing the actual plastic response of metal crystals than conventional rate‐dependent modeling in cases where the selection of active slip‐systems is essential.

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“…In Akpama et al, 44 a replacement of the nonsmooth Kuhn–Tucker conditions with a system of semismooth Fischer–Burmeister complementary functions is also presented. Recently, Prüger and Kiefer 47 have reviewed several formulations in detail and assessed their behavior for nonmonotonous loading scenarios and anisotropic hardening relations. A formulation for small strain single crystal plasticity in the context of an infeasible primal‐dual interior‐point method was proposed by Scheunemann et al 48 A different strategy for the computation of the slip rates consists in adopting a rate‐dependent regularization presented in Peirce et al, 49 Asaro and Needleman 50 and Cuitino and Ortiz, 13 which compute the slip rates with a power law‐type equation.…”

Section: Introductionmentioning

confidence: 99%

Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

Carvalho

Bortoli

Pires

2022

Numerical Meth Engineering

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A computational framework is proposed to model anisotropic metallic polycrystals subjected to mechanically induced loadings. It enables the simulation of crystal‐plasticity‐like phenomena at finite strains. The unified framework of thermodynamically consistent constitutive equations is formulated such that it couples the crystallographic slip and martensitic transformation theories. The constitutive description for the slip plasticity evolution incorporates an anisotropic hyperelastic law with self and latent‐hardening. The mechanically induced martensite formation kinematics is based on the crystallographic theory of martensitic transformations. The complete set of highly coupled equations is expressed in a single system of equations and solved by a monolithic solution procedure. It is based on the Newton–Raphson methodology and incorporates the complete linearisation leading to asymptotic quadratic rates of convergence. The quasi‐static discretized evolution equations are integrated with a fully implicit scheme, except for the critical resolved slip stresses, which employ the generalized midpoint rule. The plastic flow is integrated with an implicit exponential integrator to exactly preserve the plastic incompressibility. Viscous regularizations for both deformation mechanisms are pursued to overcome numerical difficulties and model the behavior over a wide range of strain‐rate sensitivities. Numerical examples are presented to demonstrate the efficiency and predictive capability of the methodology.

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A comparative study of integration algorithms for finite single crystal (visco-)plasticity

Cited by 14 publications

References 72 publications

Mean‐field homogenization based constitutive modeling of austenitic TRIP‐steels at the single crystal scale

Mean‐field homogenization based constitutive modeling of austenitic TRIP‐steels at the single crystal scale

Crystal plasticity algorithm based on the quasi‐extremal energy principle

Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

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